First post

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\begin{theorem}[Nullstellensatz - Weak Form]
Let k be an algebraically closed field, and let I be an ideal of the polynomial ring k[x_1, \dots, x_n]. Then:
\[
\mathcal{Z}(I) = \emptyset \quad \text{if and only if} \quad I = (1).
\]
\end{theorem}

\begin{theorem}[Nullstellensatz - Weak Form]
Let k be an algebraically closed field, and let I be an ideal of the polynomial ring k[x_1, \dots, x_n]. Then:
\[
\mathcal{Z}(I) = \emptyset \quad \text{if and only if} \quad I = (1).
\]
\end{theorem}